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\textbf{Math 366: Honors Analysis II}
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\textbf{Quiz 5}\quad \textsl{April 20, 2001}

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1.  Describe the level sets  of $F(x,y,z) = (x+y+z,x^2 + y^2 - z)$ and
determine which of them have singular points.

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2.  State:

a) The Implicit Function Theorem

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b) The Inverse Function Theorem

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c) The theorem on representing level sets locally as the graph of a
function.

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Do two of the following:

3. Outline the proof of 2a.

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4. Use 2a to prove 2b.

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5. Use 2a to prove 2c.

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